2x is a 2nd quadrant angle. In which quadrant does x/2 lie?

Answer 1

The maximum 2x can be is 179.99999, so half of that is in the first quadrant., and half that is in the first quadrant. So it usually is.
But what if x is 460 degrees, in the second quadrant? Hmmm, well, then half is 230, or the third quadrant, and half that is in second quadrant. So if 2x is less than 179.99999, then the answer is as in the first paragraph.

Answer 2

or

2x is a 2nd quadrant angle :
--> 90° < 2x < 180°
22.5° < x/2 < 45° , which is in quadrant I